Pat the beef dry and season generously with salt and pepper. Heat the olive oil in a large Dutch oven over medium-high heat. Working in batches, sear the beef on all sides until deeply browned, about 2–3 minutes per side. Transfer the beef to a plate.
Lower the heat to medium and add the onion and garlic to the same pot. Cook for 3–4 minutes, scraping up any browned bits from the bottom of the pot.
Add the chipotle peppers, adobo sauce, cumin, Mexican oregano, smoked paprika, coriander, cinnamon, cloves, allspice, salt, and black pepper. Cook for about 1 minute, stirring constantly, until the spices are fragrant.
Pour in the beef broth, orange juice, lime juice, and apple cider vinegar. Stir well, scraping the bottom of the pot to loosen any remaining browned bits.
Cover the pot and transfer it to a 325°F oven. Cook for 3–3½ hours, or until the beef is incredibly tender and easily pulls apart with a fork.
Once finished, remove the beef from the cooking liquid and shred it with two forks. Return the shredded beef to the pot and toss it with plenty of the flavorful braising juices.
While the beef cooks, add the sour cream, mayonnaise, pickled jalapeños, pickled jalapeño brine, lime juice, garlic, and salt to a blender or food processor. Blend until completely smooth and creamy, about 30–45 seconds. If the crema is too thick to drizzle, blend in 1–2 tablespoons of water until it reaches your desired consistency.
Heat a dry skillet or griddle over medium-high heat. Warm the tortillas for about 20–30 seconds per side, until soft and lightly charred around the edges. Keep them wrapped in a clean kitchen towel so they stay warm while you assemble the tacos.
Fill each warm tortilla with a generous amount of barbacoa. Drizzle over the pickled jalapeño crema, then pile on the pickled onions and plenty of fresh cilantro.